Classic Apps Tutorials

Welcome to [url=https://www.geogebra.org/classic]GeoGebra Classic[/url]! Learn how to use this integrated bundle of math apps for graphing, geometry, 3D, algebra (CAS), data (spreadsheet) and probability. Choose one of the quick and easy tours in the chapters below and get started with our apps.

How to Graph Functions and Coordinates

Create new objects

[size=100]You may create new objects (e.g. points, lines, functions) by either using the [i]Graphics Tools[/i] provided in the [i]Toolbar[/i], or by entering their equations and coordinates into the[i] Algebra Input[/i] and pressing the [i]Enter [/i]key.[br][/size]

Instructions

[size=100][table][tr][td nowrap][code]y = 3 x + 1﻿[/code][/td][td]﻿﻿Enter the linear equation [code]y = 3*x + 1 [/code]into the [i]Algebra Input[/i] and press the [i]Enter [/i]key.[/td][/tr][tr][td nowrap][code]﻿﻿f(x) = x² + 2[/code][/td][td]﻿Enter the function [code]f(x) = x^2 + 2[/code] into the [i]Algebra Input[/i] and press the [i]Enter [/i]key.[/td][/tr][tr][td nowrap]﻿﻿[code]B = (2, 1)[/code][/td][td]﻿Enter [code]B = (2, 1)[/code] into the [i]Algebra Input[/i] and press [i]Enter [/i]in order to create a new point. Create another new point [code]C = (-1, 3)[/code][/td][/tr][tr][td][center]﻿[icon]https://tube.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/center][/td][td]﻿Select the [i]Line [/i]tool from the [i]Toolbar [/i]and click twice in the [i]Graphics View[/i] or on the two existing points [i]B[/i] and [i]C[/i] to create a line.[/td][/tr][/table][br][/size][u]Hint[/u]: Click on the [img]https://wiki.geogebra.org/uploads/thumb/d/dc/Keyboard_open.svg/20px-Keyboard_open.svg.png[/img] keyboard icon in order to open a [b]virtual keyboard[/b].

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Modify existing objects

[size=100]You can drag existing objects in the [i]Graphics View[/i], or change their equations and coordinates in the [i]Algebra View[/i].[br][br][/size][table][tr][td][size=100]﻿1.[/size][/td][td][size=100]﻿[icon]https://tube.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]﻿Select the [i]Move [/i]tool and drag objects in the [i]Graphics View[/i] to change their position.[/size][/td][/tr][tr][td][size=100]﻿2.[/size][/td][td][br][/td][td][size=100]﻿Double click on an object in the [i]Algebra View[/i] in order to directly change its equation or coordinates, or redefine it.[/size][/td][/tr][/table][size=100][br][/size]

Delete objects

[size=100]Sometimes, you may want to delete objects that you created in one of the following ways:[br][/size][list][*][size=100]Select the [img]https://wiki.geogebra.org/uploads/thumb/3/38/Menu-edit-undo.svg/16px-Menu-edit-undo.svg.png[/img] [i]Undo [/i]button in order to undo the last object(s) you created.[/size][/*][*][size=100]Use the [img]https://wiki.geogebra.org/uploads/thumb/8/86/Mode_delete.svg/16px-Mode_delete.svg.png[/img] [i]Delete[/i] tool in order to delete any object you created.[br][u]Hint[/u]: Click on the last [i]Tool[/i] icon in order to open the corresponding [i]Toolbox[/i]. Select the [img]https://wiki.geogebra.org/uploads/thumb/8/86/Mode_delete.svg/16px-Mode_delete.svg.png[/img] [i]Delete [/i]tool from the [i]Toolbox[/i] and click on the object(s) you want to delete.[/size][/*][/list][size=100][br][/size]

How to Use GeoGebra's 3D Graphics Tools

What are Tools?

[size=100]GeoGebra's [i]3D Graphics View [/i]provides a [i]Toolbar [/i]with a selection of [i]Tools[/i]. You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][br][b]Task[/b]: Create a sphere using the [icon]/images/ggb/toolbar/mode_sphere2.png[/icon] [i]Sphere with Center through Point[/i] tool.[br][/size][list=1][*][size=100]Select the tool [img]https://wiki.geogebra.org/uploads/thumb/6/65/Mode_sphere2.svg/16px-Mode_sphere2.svg.png[/img] [i][i]Sphere with Center through Point[/i][/i] from the [i]3D Graphics View Toolbar[/i].[/size][/*][*][size=100]Click twice in the [i]3D Graphics View[/i] in order to create a sphere.[/size][/*][*][size=100]Select the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move [/i]tool and drag the points in order to change the sphere's size and / or position.[/size][/*][/list]

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How to move objects in the 3D coordinate system

[size=100]In order to move a point in the three-dimensional coordinate system, you can [b]switch between two modes[/b] by repeatedly clicking on the point while the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move[/i] tool is activated:[br][list][*][b]Mode [i]xOy[/i]-plane[/b]: You may move the point parallel to the [i]xOy[/i]-plane without changing the [i]z[/i]-coordinate.[/*][*][b]Mode [i]z[/i]-axis[/b]: You may move the point parallel to the [i]z[/i]-axis without changing the [i]x[/i]- and [i]y[/i]-coordinates. [/*][/list][/size]

What are Toolboxes?

[size=100]GeoGebra's [i]Tools[/i] are organized in [i]Toolboxes[/i], containing similar [i]Tools [/i]or [i]Tools [/i]that generate the same type of new object. You can [b]open a [/b][i][b]Toolbox[/b] [/i]by clicking on a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][br][b]Task[/b]: Create a cube using the [icon]/images/ggb/toolbar/mode_cube.png[/icon] [i]Cube[/i] tool.[br][/size][list=1][*][size=100]Search the [i]Toolboxes [/i]for the [img]https://wiki.geogebra.org/uploads/thumb/d/d3/Mode_cube.svg/16px-Mode_cube.svg.png[/img] [i]Cube[/i][i] [/i]tool.[br][/size][/*][*][size=100]Click twice in the [i]3D Graphics View[/i] in order to create a cube.[/size][br][/*][*][size=100]Select the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move [/i]tool and drag the points in order to change the cube's size and / or position.[br][/size][/*][/list]

What are Tooltips?

[size=100]If you select a [i]Tool[/i], [b]a [i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: When you click on a [i]Tooltip[/i], a web page providing help for the selected [i]Tool [/i]opens in your browser window.[br][br][b]Task[/b]: Create a pyramid using the [icon]/images/ggb/toolbar/mode_pyramid.png[/icon] [i]Pyramid [/i]tool works[br][/size][list=1][*][size=100]Select the [img]https://wiki.geogebra.org/uploads/thumb/0/05/Mode_pyramid.svg/16px-Mode_pyramid.svg.png[/img] [i][size=100][i]Pyramid [/i][/size] [/i]tool.[/size][/*][*][size=100]Read the [i]Tooltip.[/i][/size][/*][*][size=100]Figure out how to use this tool in order to create a pyramid.[/size][br][/*][/list]

How to Use GeoGebra's CAS Tools

What are Tools?

[size=100]GeoGebra provides a [i]Toolbar [/i]with a selection of [i]Tools [/i]specific for the CAS [i]View[/i]. You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][br][b]Task[/b]: Solve an equation using the [icon]/images/ggb/toolbar/mode_solve.png[/icon] [i]Solve[/i] tool[/size][list=1][*][size=100]Type the equation [code]3x + 1 = 10[/code] into the [i]CAS Input[/i].[/size][/*][*][size=100]Select the [img]https://wiki.geogebra.org/uploads/thumb/a/a9/Mode_solve.svg/16px-Mode_solve.svg.png[/img] [i]Solve[/i] tool from the [i]CAS View Toolbar[/i].[br][u]Note[/u]: The equation is solved and the solution is shown underneath the equation.[/size][/*][/list]

Try it yourself...

What are Tooltips?

[size=100]If you select a [i]Tool[/i], a [b][i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: Click on a [i]Tooltip[/i] in order to open a web page providing help for the selected [i]Tool[/i].[br][br][/size][b]Task[/b]: Factorize the term [code](x² - 4)[/code] using the [icon]/images/ggb/toolbar/mode_factor.png[/icon] [i]Factor [/i]tool.

How to Input Data and Refer to Cells

Entering data and creating objects

[size=100]In GeoGebra’s [i]Spreadsheet View[/i] every cell has a specific name that allows you to directly address each cell.[br][u]Example[/u]: The cell in column [i]A[/i] and row [i]1[/i] is named [b]A1[/b].[br][br]You may use the [i]Spreadsheet [/i]cells in order to create mathematical objects that are directly displayed in the [i]Graphics View[/i] (e.g. points).[br][br][b]Task 1[/b][br][/size][table][tr][td][size=100]1.﻿[/size][/td][td][center][size=100][b]A1[/b][/size][/center][/td][td][size=100]﻿[font=Arial]Enter the number [/font][code]10 [/code]into cell [b]A1[/b].[br][u]Hint[/u]: Always confirm your input by pressing the [i]Enter[/i] key.[/size][/td][/tr][tr][td][size=100]﻿2.[/size][/td][td][center][size=100][b]B1﻿[/b][/size][/center][/td][td][size=100]﻿Enter the coordinates [code](-2, 2) [/code]into cell [b]B1[/b].[br][u]Note[/u]: The point [i]B1 = (-2, 2)[/i] is automatically shown in the [i]Graphics View[/i].[/size][/td][/tr][tr][td][size=100]3.[br][/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][br][/size][/td][td][size=100]Select the [i]Move[/i] tool and drag point [i]B1[/i] in the [i]Graphics View[/i]. [br][u]Note[/u]: The [i]Spreadsheet View [/i]shows the current position of point [i]B1 [/i]in cell [b]B1[/b][i][/i].[br][/size][/td][/tr][tr][td][size=100]4.[br][/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_delete.png[/icon][br][/size][/td][td][size=100]Delete the content of cell [b]B1[/b].[/size][/td][/tr][/table]

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Cell references

[size=100]You may refer to another cell by using its name in your new input.[br][u]Note[/u]: If the content of this cell is modified, the new input adapts automatically.[br][/size][size=100][br][b]Task 2[/b][br][/size][table][tr][td][size=100]1.﻿[/size][/td][td][size=100][b]A1[/b][/size][/td][td][size=100]﻿Change the number in cell [b]A1[/b] to [code]1.5[/code] and confirm your input.[/size][/td][/tr][tr][td][size=100]﻿﻿2.[/size][/td][td][center][size=100]﻿[b]B1[/b]﻿[/size][/center][/td][td][size=100]﻿Enter the formula [code]= 2 * [/code]into cell [b]B1[/b] and then select cell [b]A1[/b] in order to insert its name into the formula. Confirm your input.[br][u]Note[/u]: GeoGebra calculates [i]2 * 1.5[/i] and displays the solution [i]3[/i] in cell [b]B1[/b].[br][/size][/td][/tr][tr][td][size=100]3.[br][/size][/td][td][b][size=100][/size][/b][center][size=100][b]A1[/b][br][/size][/center][/td][td][size=100]﻿﻿﻿Change the content of cell [b]A1[/b] to [font=monospace]3[/font].[br][u]Note[/u]: The content of cell [b]B1[/b] automatically adapts to your changes.[/size][/td][/tr][/table][size=100][br][br][b]Task 3[/b][br][table][tr][td]1.﻿[/td][td][b]C1[/b][/td][td]Enter the coordinates [code](A1, B1) [/code]into cell [b]C1[/b] and confirm your input.[br][u]Hint[/u]: Cell [b]C1[/b][i] now [/i]shows the coordinates [i](3, 6)[/i]. The corresponding Point [i]C1[/i] is automatically displayed in the [i]Graphics View[/i].[/td][/tr][tr][td]2.﻿[/td][td][b]A1[/b][/td][td]﻿Change the value of cell [b]A1[/b] to [code]2[/code].[br][u]Note[/u]: The coordinates in cell [b]C1[/b] and the corresponding point automatically adapt to your changes.[/td][/tr][/table][/size]

Probability

Take a quick and easy tour through this chapter to learn about [url=https://www.geogebra.org/classic/probability]GeoGebra Classic - Probability[/url] and get to know the probability and statistics calculator.

How to use the Probability Calculator

What is the Probability Calculator?

[size=100]The [i]Probability Calculator[/i] allows you to graph and explore a variety of probability distributions. Just select your preferred distribution (e.g. Normal distribution, Binomial distribution) and customize it by adjusting the parameters.[br][br][/size][u]Note[/u]: Each distribution has specific parameters you need to adjust (e.g. Normal distribution with mean [math]\mu[/math] and standard deviation [math]\sigma[/math]).

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Features of the Probability Calculator

[table][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/1/1b/Probability_calculator_interval_between.svg/180px-Probability_calculator_interval_between.svg.png[/icon]﻿[/td][td]Calculate the probability P([i]a[/i] [math]\le [/math]X [math]\le[/math] [i]b[/i]) of a distribution.[u]Note[/u]: You may adjust the interval limits [i]a[/i] and [i]b[/i] by either replacing their values in the formula, or by dragging them in the graph.﻿[br][/td][/tr][tr][td]﻿[icon]https://wiki.geogebra.org/uploads/thumb/9/98/Probability_calculator_interval_left.svg/180px-Probability_calculator_interval_left.svg.png[/icon][/td][td]﻿Calculate the probability P(X[math] \le [/math][i]x[/i]) of a left sided distribution. [/td][/tr][tr][td]﻿[icon]https://wiki.geogebra.org/uploads/thumb/e/e5/Probability_calculator_interval_right.svg/180px-Probability_calculator_interval_right.svg.png[/icon][/td][td]﻿Calculate the probability P([i]x[/i][math] \le [/math]X) of a right sided distribution. [/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/6/60/Probability_calculator_cumulative_distribution.svg/120px-Probability_calculator_cumulative_distribution.svg.png[/icon]﻿[/td][td]﻿Toggle between the graphs of the [i]probability density function[/i] and the [i]cumulative distribution function[/i].[/td][/tr][/table]

Exam Mode

The Exam Mode allows your students to use GeoGebra during exams without being able to access the Internet or any other software installed on the computer. Leaving the GeoGebra window in any way triggers an alert, which can easily be spotted by the teacher and is also documented in the Exam Log.

What is GeoGebra Exam?

[img]https://wiki.geogebra.org/uploads/thumb/9/9d/Menu_view_exam.svg/16px-Menu_view_exam.svg.png[/img] GeoGebra Exam allows you and your students to use the power of GeoGebra during exams on paper (i.e. like a graphing calculator or pocket calculator) while restricting their access to the Internet or other software that should not be used during the exam.[br][br][img]https://wiki.geogebra.org/uploads/thumb/9/9d/Menu_view_exam.svg/20px-Menu_view_exam.svg.png[/img] GeoGebra Exam...[br][list][*]... can easily be accessed at [url=https://www.geogebra.org/exam]https://www.geogebra.org/exam[/url]﻿[/*][*]... runs in your browser, so no additional installations are required.[/*][*]... can be customized in case your students should not have access to the full power of GeoGebra (e.g. deactivate the GeoGebra CAS)[/*][*]... runs in full screen mode allowing no space for other information to be displayed on screen.[br][/*][*]... doesn't allow access to the Internet, the GeoGebra Materials platform, or files saved on the computer.[/*][/list]

GeoGebra Exam activated

GeoGebra Exam Alert

Leaving the [img]https://wiki.geogebra.org/uploads/thumb/9/9d/Menu_view_exam.svg/16px-Menu_view_exam.svg.png[/img] GeoGebra Exam window triggers a visual alert that is easily detectable and recorded in the Exam Log.